Final answer:
The capacitance range needed for an RLC circuit to tune between 500 and 1650 kHz with a fixed inductor of 1.00 µH is approximately 0.625 to 2.05 µF, which corresponds to option c.
Step-by-step explanation:
To calculate the range of capacitance needed for an RLC circuit to resonate at frequencies between 500 and 1650 kHz with a fixed inductor of 1.00 µH, we use the resonance formula of an LC circuit:
f = \frac{1}{2\pi\sqrt{LC}}
Where:
- f is the resonant frequency
- L is the inductance
- C is the capacitance
To find the capacitance range, we rearrange this equation to solve for C:
C = \frac{1}{(2\pi f)^2 L}
Calculating the capacitance for the lower frequency limit (500 kHz) and the higher frequency limit (1650 kHz), we get:
- C for 500 kHz: C = \frac{1}{(2\pi 500 \times 10^3)^2 \times 1 \times 10^{-6}} Highly approximated to ≈ 2.05 µF
- C for 1650 kHz: C = \frac{1}{(2\pi 1650 \times 10^3)^2 \times 1 \times 10^{-6}} Highly approximated to ≈ 0.625 µF
Thus, the required range of capacitance is from approximately 0.625 to 2.05 µF, making option c the correct option in the final answer.